Question: Omar is 4 times as old as Vanessa. Six years ago, Omar was 6 times as old as Vanessa. How old is Vanessa now?
Solution: We can use the given information to write down two equations that describe the ages of Omar and Vanessa. Let Omar's current age be $o$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $o = 4v$ Six years ago, Omar was $o - 6$ years old, and Vanessa was $v - 6$ years old. The information in the second sentence can be expressed in the following equation: $o - 6 = 6(v - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $o$ and substitute it into our second equation. Our first equation is: $o = 4v$ . Substituting this into our second equation, we get: $4v$ $-$ $6 = 6(v - 6)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $4 v - 6 = 6 v - 36$ Solving for $v$ , we get: $2 v = 30.$ $v = 15$.